Horizontal Flat Plate Research Articles

LAMINAR FORCED CONVECTION IN HORIZONTAL CHANNEL WITH HEAT GENERATION PLATES COOLED BY WATER

This paper describes the study of the behavior of two-dimensional and parallel horizontal flat plates with uniform internal heat generation subjected to laminar forced convection of water. The governing equations are solved numerically using the finite volume technique with Power-Law interpolating scheme and the SIMPLE algorithm. After the simulations the temperature and velocity fields were obtained for various plates spacing and fluid inlet velocities, as well as the Nusselt number values.

Void waves propagating in the bubbly two-phase turbulent boundary layer beneath a flat-bottom model ship during drag reduction

The injection of bubbles into a turbulent boundary layer can reduce the skin friction of a wall. Conventionally, the drag reduction rate is evaluated using time-averaged quantities of the mean gas flow rate or mean void fraction. Actually, as bubbles are subject to strong shear stresses near the wall, void waves and local bubble clusters appear. For pipe and channel flows, such wave-like behavior of the dispersed phase has been investigated intensely as an internal two-phase flow problem. We investigate how this wavy structure forms within the boundary layer as an external spatially developing two-phase flow along a horizontal flat plate. We describe how our model ship is designed to meet that purpose and report bubble-traveling behavior that accompanies unexpectedly strong wavy oscillations in the streamwise direction. A theoretical explanation based on a simplified two-fluid model is given to support this experimental fact, which suggests that void waves naturally stand out when drag reduction is enhanced through the local spatial gradient of the void fraction.

Numerical Study of the Forced Convective Condensation on a Short Vertical Plate

ABSTRACTNumerical investigation was conducted on the effects of gravity, surface tension, and wall adhesion upon condensation on a short vertical plate. The volume of fluid method was applied to model the interaction between the liquid and vapor phases and to capture the interface. The surface tension was implemented by employing the method of continuum surface force model. A modified phase-change model, derived from basic equations related to the kinetic gas theory, was proposed and verified based on the cases of Nusselt film condensation of water vapor on a vertical flat plate, the forced convection film condensation on a horizontal flat plate, and the capillary blocking due to condensation in a horizontal miniature circular tube. The predicted results showed that a laminar capillary wavy flow regime exists and the waves enhance the heat transfer of condensation on the plate. The mean film thickness increases and the heat transfer performance becomes worse with decrease of gravity. A high value of surface tension or contact angle, representing a large surface free energy difference, leads to an enhancement of heat transfer on the plate with large-amplitude waves.

B-spline collocation and quasi-interpolation methods for boundary layer flow and convection heat transfer over a flat plate

The B-spline collocation methods and a new ODEs solver based on B-spline quasi-interpolation are developed to study the problem of forced convection over a horizontal flat plate, numerically. The problem is a system of nonlinear ordinary differential equations which arises in boundary layer flow. A more accurate value of $$\sigma =f^{\prime \prime }(0)$$?=f?(0) obtained by applying quartic B-spline collocation method and utilized to solve the system of ODE. The results are shown to be precise as compared to the corresponding results obtained by Howarth.

Experimental investigation of nanofluid free convection over the vertical and horizontal flat plates with uniform heat flux by PIV

This paper applies the particle image velocimetry (PIV) to measure the laminar boundary layer thickness of TiO2–water nanofluid free convection over the vertical and horizontal flat plates with constant heat flux. The results are presented for two values of heat flux strength equal to 3000 and 7000w/m2. The effects of nanoparticles and heat flux strength on the boundary layer thickness and velocity profiles are investigated in details. Finally, a comparison is performed between the experimental, theoretical and numerical results for different conditions. The obtained results revealed that the velocity boundary layer decreases by adding the nanoparticles to the base fluid. These reductions, at ϕ=0.1%, are in the vicinity of 7.5% and 5.2% for q″=3000and7000wm-2, respectively. Also, the maximum reductions in the vertical velocity component by adding the nanoparticles at ϕ=0.1% are in the vicinity of 4% and 3.3% for q″=3000and7000wm-2, respectively.

Numerical and experimental investigation of flow structure and behavior of nanofluids flow impingement on horizontal flat plate

Numerical and experimental studies have been conducted to investigate flow structure and heat transfer of nanofluid jet normally impinging on a flat plate. Al2O3–water is used as working fluid. The governing equations are numerically solved using finite volume approach together with SIMPLER algorithm. A wide spectrum of experimental and numerical simulations has been done. The results covered wide ranges of Reynolds number, Re, from 3000 to 32,000, nanofluid volume fraction, ϕ, from 0 to 10%. The dimensionless distance from jet nozzle to the horizontal plate was kept constant at 3. An experimental apparatus was constructed to measure the film thickness distribution, wall temperature and temperature of flowing fluid. The effects of Re and ϕ are investigated on the film thickness distribution, isothermal contours, and both local and average Nusselt numbers. A good agreement was found between the numerical and experimental results as well as the previous cited results. The results showed that the increasing of nanoparticle percent increases the convective heat transfer coefficient compared with the pure water. At ϕ=10.0% and Re=24,000 the heat transfer coefficient increases by 62% compared with the pure water. The effect of nanofluid type (Al2O3–TiO2–CuO) is studied numerically. It has been observed that the CuO nanofluid increases the heat transfer by 8.9% and 12% compared to aluminum and titanium nanofluid respectively.

Interaction of two spark-generated bubbles near a confined free surface

In this paper, the oscillation of two spark-generated bubbles placed on a vertical column in close proximity to a confined free surface is considered. The confined free surface is accorded by the top opening of different configurations. These configurations include (i) a centrally perforated horizontal flat plate ( $${\theta=90^{\circ})}$$ , (ii) vertically placed cylinder ( $${\theta=0^{\circ})}$$ and (iii) nozzle ( $${\theta >0^{\circ})}$$ . The main objective of the present work is to study the effects of key parameters such as the nozzle geometry, the locations of the energy input (i.e., initial position of the bubbles with respect to each other and relative to the free surface) on the dynamics of the two bubbles and the free surface. It was found that the lifetime of the upper bubble decreases from the vertical cylinder to the flat plate case. In addition, by reducing the inter-bubble distance, the lifetime of the upper bubble becomes longer and the repulsion between two bubbles during the expansion phase is stronger. Finally, by reducing the upper bubble-free surface distance, the repulsion between two bubbles during expansion phase increases, the tendency of the upper bubble to rebound and initiate another oscillation cycle decreases, and the amplitude of elevation of the free surface increases.

The Couette–Poiseuille flow of a suspension modeled as a modified third-grade fluid

In this paper, we modify the thermodynamically compatible third-grade fluid model by introducing a shear-rate- and volume-fraction-dependent viscosity into the equation. With this new model, it is possible to predict not only the normal stress differences, but also the variable viscosity observed in many suspensions. We study the Couette–Poiseuille flow of such a fluid between two horizontal flat plates. The steady fully developed flow equations are made dimensionless and are solved numerically; the effects of different dimensionless numbers are discussed.

Application of Adomian Method for the Magnetic field effects on mass transport at vertical cylindrical electrode

Magnetic forced convective mass transfer onto cylindrical electrode placed in a uniform horizontal magnetic field is considered. The study is based on polarization curves and chronoamperometry measurements during oxidation or reduction of ferri-ferrocynide system at various bulk concentrations. In the case of platinum electrode with different diameter and cylinder length, the obtained results show an increase of the mass transfer rate similar to that observed on horizontal or vertical flat plates. The enhancements of the limiting diffusion current depend on the magnetic field strength; the bulk electroactive species concentration and cylindrical electrode diameter and length have been quantified. Based on Adomian decomposition method (ADM), a detailed theoretical analysis of the mass transfer process is undertaken, and expressions are obtained which predict with good accuracy the observed experimental data.

Effects of Shear Dependent Viscosity and Variable Thermal Conductivity on the Flow and Heat Transfer in a Slurry

In this paper we study the effects of variable viscosity and thermal conductivity on the heat transfer in the pressure-driven fully developed flow of a slurry (suspension) between two horizontal flat plates. The fluid is assumed to be described by a constitutive relation for a generalized second grade fluid where the shear viscosity is a function of the shear rate, temperature and concentration. The heat flux vector for the slurry is assumed to follow a generalized form of the Fourier’s equation where the thermal conductivity k depends on the temperature as well as the shear rate. We numerically solve the governing equations of motion in the non-dimensional form and perform a parametric study to see the effects of various dimensionless numbers on the velocity, volume fraction and temperature profiles. The different cases of shear thinning and thickening, and the effect of the exponent in the Reynolds viscosity model, for the temperature variation in viscosity, are also considered. The results indicate that the variable thermal conductivity can play an important role in controlling the temperature variation in the flow.

BIOCONVECTIVE NON-NEWTONIAN NANOFLUID TRANSPORT IN POROUS MEDIA CONTAINING MICRO-ORGANISMS IN A MOVING FREE STREAM

Bioconvection flow of non-Newtonian nanofluids along a horizontal flat plate in a porous medium saturated with gyrotactic microorganisms is investigated by combined group similarity numerical technique. A linear group of transformations is used to develop similarity transformations and the corresponding similarity equations of the governing coupled, nonlinear ordinary differential boundary layer transport equations. The resulting nonlinear boundary value problem with appropriate boundary conditions is solved numerically by an MAPLE software algorithm. The effects of the controlling parameters on the flow, heat, nanoparticle concentration and the density of motile microorganisms characteristic as well as on the local Nusselt, Sherwood and the motile microorganism numbers have been examined. It is found that the bioconvection parameters have strong effects on the flow, heat and mass transfer and motile microorganism numbers. The present study finds application in microbial fuel cells.

Heat transfer analysis and flow of a slag-type fluid: Effects of variable thermal conductivity and viscosity

In this paper we study the effects of variable viscosity and thermal conductivity on the heat transfer and flow of a slag-type non-Newtonian fluid between two horizontal flat plates. We solve the governing equations in their non-dimensional forms and perform a parametric study to see the effects of various dimensionless numbers on the velocity, volume fraction and temperature profiles. The different cases of shear- thinning and thickening, and the effect of the exponent in the Reynolds viscosity model, for the temperature variation in viscosity, are also considered.

Heat Flux Controlled Pool Boiling of Zirconia–Water and Silver–Water Nanofluids on a Flat Plate: A Coupled Map Lattice Simulation

In the present work, the characteristic atmospheric saturated heat flux controlled pool boiling curves for zirconia–water and silver–water nanofluids have been reproduced by the coupled map lattice (CML) method using a two-dimensional (2D) boiling field model. The heater is a long horizontal flat plate of thickness 0.44 mm. The pool height is 0.7 mm. The stirring action of the bubbles is modeled by increasing the fluid thermal diffusivity by an enhancement factor. The thermal conduction in the plate is also incorporated into the model. The basic advantage of CML is that individual bubbles are not tracked, and yet the effects of bubbles are reflected qualitatively in the final solution. In the simulation of atmospheric saturated pool boiling of water minimum cavity diameter taken is 0.8 μm based on which a random distribution of cavity sizes has been specified. In the boiling of ZrO2–water nanofluid there is a deposition of nanoparticles in the cavities on the heated surface resulting in reduction of surface roughness. This feature is taken care of by proportionate decrease in minimum cavity diameter. The CML model predicts decrease in heat transfer coefficient and increase in critical heat flux (CHF) with increase in zirconia nanoparticle concentration. In the case of Ag–water nanofluid no such deposition of nanoparticles has been reported; rather surface oxidation occurs which increases the surface roughness. This is simulated by proportionately increasing the minimum cavity diameter with weight fractions of nanoparticles. The present CML model predicts increase in the heat transfer coefficient and decrease in CHF with increase in silver nanoparticle concentration. Thus, the CML results for the boiling of the aforesaid two nanofluids match qualitatively with the published experimental works.

Numerical Simulation of Two-dimensional Forced Convective Film Boiling Flow over a Horizontal Flat Surface

In this numerical study, a Coupled Level Set and Volume of Fluid (CLSVOF) interface capturing method with multi-directional advection algorithm is used to investigate the flow and heat transfer characteristics of a two-dimensional, incompressible, laminar, forced convective saturated film boiling over an isothermal horizontal flat plate. In this study, the effects of wall superheats and liquid free stream velocities are considered for water and refrigerant R-134a. In the numerical simulation of forced convection saturated film boiling flows, the wall shear stress and the heat transfer coefficient results are evaluated with Cess and Sparrow1 correlations developed based on the boundary layer approximations. The numerical results show good agreement with the correlations developed based on the boundary layer theory. Both heat transfer coefficient and wall shear stress are strongly dependent on the wall superheats and inflow free stream velocities.

Experiments and calculations of cnoidal wave loads on a flat plate in shallow-water

Horizontal and vertical wave forces due to the interaction of cnoidal waves with a two-dimensional, horizontal flat plate located in shallow-water are studied through laboratory experiments and calculations. The experiments are conducted for a combination of two water depths, five wavelengths and four wave heights, corresponding to the propagation of nonlinear waves in shallow-water depth. The model is located at six different elevations and submergence depths such that all possible cases of a coastal bridge deck fully above the still-water level, a deck on the surface and a fully submerged deck are considered in the study. Calculations are performed for the same cases as in the laboratory experiments and include the results of a nonlinear shallow-water wave model based on the Level I Green–Naghdi equations for the fully submerged cases, and Euler’s equations coupled with the Volume of Fluid interface tracking method for one submerged case, one elevated case, and one case at the water surface. Comparison of existing theoretical solutions are also provided, including the Long-Wave Approximation based on linear potential theory for the submerged cases, and empirical relations for the elevated cases. The set of data presented here provides an insight into storm wave loads on the decks of coastal bridges, jetties and piers located in shallow-water areas.

Effect of Velocity Profile on the Stability of Liquid Sheet

An electrified liquid sheet injected into a dielectric moving through a viscous gas bounded by two horizontal parallel flat plates of a transverse electric field is investigated with the linear analysis method. The liquid sheet velocity profile and the gas boundary layer thickness are taken into account. The relationship between temporal growth rate and the wave number was obtained using linear stability analysis and solved using the Chebyshev spectral collocation method. The effects of the velocity profile on the stability of the electrified liquid sheet were revealed for both sinuous mode and varicose mode. The results show that the growth rate of the electrified Newtonian liquid is greater than that of corresponding Newtonian one under the same condition, and the growth rate of the sinuous mode is greater than that of the varicose mode. Keywords: instability; planar liquid sheet; velocity profile;spectral method;linear analysis

Experimental Investigation of Heat Transfer for a Jet Impinging Obliquely on a Flat Surface

An experimental study investigated the effects of the inclination of an impinging circular jet on heat transfer from a horizontal flat plate. Local Nusselt number distribution was determine depending on inclination angle, jet-to-plate distance, and Reynolds number. The results show that the maximum heat transfer point moves toward the uphill side of the plate and that the maximum heat transfer decreases as the inclination angle decreases. The correlations were conducted to predict maximum and local Nusselt number as a function of Re, θ, L/D, and x/D for three specific regions.

Flow of granular materials with slip boundary condition: A continuum–kinetic theory approach

We study the steady fully developed flow of granular materials between two horizontal flat plates, subject to slip at the walls. The constitutive model for the stress tensor is based on ideas in continuum mechanics and kinetic theory. The constitutive equation used in our study is a model proposed by Rajagopal et al. (1994) [24], and the material properties such as viscosity and the normal stress coefficients are derived using the kinetic theory approximation proposed by Boyle and Massoudi (1990) [2] which includes the effect of the gradient of volume fraction. The slip boundary condition is based on the particle dynamics simulation results of Rosato and Kim (1994) [30]. The governing equations are non-dimensionalized, and the resulting system of non-linear differential equations is solved numerically. The results for the velocity profiles and the volume fraction profiles are presented.

An experimental investigation on a solar still with an integrated flat plate collector

This work promotes the performance of the single basin solar still by means of preheating the saline water using an integrated flat plate collector arrangement. A conventional single slope single basin still and a single slope flat plate collector basin still (FPCB still) are fabricated with the same basin area of 1m2. The FPCB still is fabricated similar to a conventional still, with the integration of a horizontal flat plate collector arrangement to form six small compartments in the basin. The projected space between the consecutive basins acts as an extended surface which increases the temperature of the basin as well as the flat plate collector where the saline water is preheated before it enters the basin. Due to separate compartments (absorber plate) in the basin, the mass of water reduces and the evaporation rate increases for the same depth of water in the basin. Experiments are carried out by varying the water depth in the basin and using the wick and energy storing materials in basins of both stills. The FPCB still gives about 60% higher distillate than the conventional still for the same basin condition. Economic analysis shows that the cost of distilled water for the FPCB still is lower than that for the conventional still.

To Study Different Losses and Loss Co-Efficient on Solar Flat Plate Collector at 900 Yaw Angle

The flat plate collector is a device used for harnessing the solar energy. The efficiency of this device is dependent on the various heat losses. These losses are bottom loss, side loss, edge loss, corner loss, sealing loss & top loss. These losses are measured as well as recorded. There are forty eight thermocouples located at different points. The input energy is through the electric heaters to the collector. These heaters are kept below the absorber. The capacity of each heater is 0.5 kW. These heaters are two in number. The wind velocity is measured by the vane type anemometer. The input heat flux is kept constant & wind velocity is varied. The evaluation of various heat losses is important for the performance evaluation of the collector. Generally the upward heat losses play an important role in the total heat losses. The present paper is an experimental simulation of a horizontal single glazed flat plate collector. The losses are measured under steady state conditions at different wind velocity & keeping 900yaw angle and at zero tilt angle.